A certain chromosome defect occurs in only 1 in 250 adult Caucasian males. A ran

Question

A certain chromosome defect occurs in only 1 in 250 adult Caucasian males. A random sample of n = 100 adult Caucasian males is to be obtained.

(a) What is the mean value of the sample proportion p, and what is the standard deviation of the sample proportion? (Enter your mean as an exact integer, fraction, or decimal. Round your standard deviation to five decimal places.)

(b) Does p have approximately a normal distribution in this case? Explain.

Yes, because np < 10 and n(1 p) < 10.Yes, because np > 10 and n(1 p) > 10.    No, because np < 10.No, because np > 10.

(c) What is the smallest value of n for which the sampling distribution of p is approximately normal?
n =  adult Caucasian males

Explanation / Answer

Answer to the question below:

a.

Mean = np = 100*1/250 = 0.4

Standard deviation = sqrt(100*1/250*249/250) = .631

b. np = 100*1/250 = .4 <10 and n(1-p) = 100(249/250) >10

So, ansswer is 3rd option : because np < 10.

c. The smallest value be n

n(1/250) >=10

n >= 2500

So, smallest value of n should be 2500 for p^ to be approx. normal.

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